论文标题
Galkin的下限猜想对司法
Galkin's lower bound conjecture holds for the Grassmannian
论文作者
论文摘要
令gr $（k，n）$为司法。量子乘法乘以第一个Chern类$ c_1（{\ rm gr}（k，n））$诱导内态性$ \ hat c_1 $ c_1 $的c_1 $ c_1 $ of有限维矢量空间$ \ mathrm {qH}我们的主要结果是，Galkin的猜想成立。它指出，$ \ hat {c} _1 $的最大真实特征值大于或等于$ \ dim {\ rm gr}（k，k，n）$+1具有均等的$+1时，仅当Gr $（K，N）= \ MathBb {p}^{N-1} $时。
Let Gr$(k,n)$ be the Grassmannian. The quantum multiplication by the first Chern class $c_1({\rm Gr}(k,n))$ induces an endomorphism $\hat c_1$ of the finite-dimensional vector space $\mathrm{QH}^*({\rm Gr}(k,n))_{|q=1}$ specialized at $q=1$. Our main result is a case that a conjecture by Galkin holds. It states that the largest real eigenvalue of $\hat{c}_1$ is greater than or equal to $\dim {\rm Gr}(k,n)$+1 with equality if and only if Gr$(k,n)=\mathbb{P}^{n-1}$.
